For its Summer 2026 term, the STOCHASTICA SNIP seminar will be held online every two weeks starting on May 13. Talks of 30-45 minutes will be followed by 15-30 minutes of open discussion. Initially, seminars will be focused on introducing new problems and applications, to stimulate further discussions and ideas within individual working groups.  

The eighth seminar will be given by Prof. Daniel Heydecker, University of Oslo, and chaired by Prof. Xuerong Mao (Action Vice-chair).

The Porous Medium Equation: Multiscale Integrability in Large Deviations

We consider a zero-range process $\eta^N_t(x)$ with superlinear local jump rate, which in a hydrodynamic-small  particle rescaling converges to the porous medium equation $\partial_t u=\frac12\Delta u^\alpha, \alpha>1$. As a main result we obtain a large deviation principle in any scaling regime $N\to \infty, \chi_N\to 0$. The key challenge is to develop uniform integrability estimate on the nonlinearity $(\eta^N(x))^\alpha$, even when the individual trajectories may be too rough to obtain regularity estimates. We resolve this by introducing a novel multiscale argument exploiting the appearance of pathwise regularity across scales.